Question

How do you figure out how many cups are in $6$ litres using dimensional analysis$?$

Answer 1

To solve the given problem we need to find the basic equation with the involvement of litres and cups. Which means we need to find how many cups are equal to one litre. Also, we need to find the conversion factor. The final answer would be in cups. Also, we need to know how to cancel the units. Also, we would use the arithmetic operation of addition/ subtraction/ multiplication/ division.

Complete step by step solution:
In this question, we need to find how many cups are in $6$ litres. We know that $1$litre is equal to$4.22675US$cups.
Which can be written as,
1L = 4.22675UScups$$$$ \to \left( 1 \right)
The above equation can also be written as,
Case: 1
$\dfrac{{1L}}{{4.22675UScups}} = 1 \to \left( 2 \right)$
Case: 2
$\dfrac{{4.22675UScups}}{{1L}} = 1 \to \left( 3 \right)$
By comparing the equation$\left( 2 \right)$and$\left( 3 \right)$, we get
$\dfrac{{1L}}{{4.22675UScups}} = \dfrac{{4.22675UScups}}{{1L}} = 1 \to \left( 4 \right)$
So, we get that the denominator term is equal to the numerator term. If the numerator term is equal to the denominator term then the conversion factor is $1$. By using the equation $\left( 4 \right)$
we can solve the given question. In the equation,$\left( 4 \right)$ we have the conversion equation for $1$ a litre.
So, according to the question we have to find the number of cups in $6$litre.
So, we multiply $6$ litre with the equation $\left( 3 \right)$,
So, we get
$6L \times \dfrac{{4.22675UScups}}{{1L}}$
In the above equation litre units cancel each other. So, we get the final value as shown below,
$6 \times 4.22675 = 25US$Cups.

Note: This type of question describes the operation of addition/ subtraction/ multiplication/ division. We would try to cancel the litre units to solve the given problem and we should get the final answer in $UScups$.
Remember that the value of litre must be in terms of $UScups$. Note that if the numerator value is equal to the denominator value, then the conversion factor will be $1$. If the conversion factor is $1$, then we won’t make changes in the volume.